# zbMATH — the first resource for mathematics

Some aspects of the spline smoothing approach to non-parametric regression curve fitting (with discussion). (English) Zbl 0606.62038
The regression model $$Y_ i=g(t_ i)+\epsilon_ i$$ is considered. Nonparametric estimation of the function g is discussed under the assumption that the design points satisfy $$t_ 1\leq t_ 2\leq...\leq t_ n$$ and that the errors $$\epsilon_ i$$ are uncorrelated with zero mean. The spline smoothing approach is described and developed. The question of providing inference regions for curves is approached via finite- dimensional Bayesian formulation. The various methods presented in the paper are illustrated by examples from different fields of application. A report of a broad discussion (43 discussants) is enclosed.
Reviewer: J.Bartoszewicz

##### MSC:
 62G05 Nonparametric estimation 62J02 General nonlinear regression 65D10 Numerical smoothing, curve fitting 65C99 Probabilistic methods, stochastic differential equations